Question

1. a plane parallel to lh

identify all pairs of each type of angles in the diagram. name the two lines and the transversal that form each pair.

1. corresponding angles
2. alternate interior angles
3. same - side interior angles
4. alternate exterior angles

Explanation:

Step1: Define corresponding angles

Corresponding angles are in the same relative position.
Pairs: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle6$, $\angle7$ and $\angle8$; lines are $d$ and $e$, transversal is $a$ for $\angle1$ - $\angle3$ and $\angle7$ - $\angle8$, transversal is $b$ for $\angle2$ - $\angle4$ and $\angle5$ - $\angle6$.

Step2: Define alternate - interior angles

Alternate - interior angles are between the two lines and on opposite sides of the transversal.
Pairs: $\angle2$ and $\angle3$, $\angle1$ and $\angle4$; lines are $d$ and $e$, transversal is $a$ for $\angle1$ - $\angle4$, transversal is $b$ for $\angle2$ - $\angle3$.

Step3: Define same - side interior angles

Same - side interior angles are between the two lines and on the same side of the transversal.
Pairs: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$; lines are $d$ and $e$, transversal is $a$ for $\angle1$ - $\angle3$, transversal is $b$ for $\angle2$ - $\angle4$.

Step4: Define alternate - exterior angles

Alternate - exterior angles are outside the two lines and on opposite sides of the transversal.
Pairs: $\angle5$ and $\angle7$, $\angle6$ and $\angle8$; lines are $d$ and $e$, transversal is $a$ for $\angle7$ - $\angle5$, transversal is $b$ for $\angle6$ - $\angle8$.

Answer:

1. Corresponding angles: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle6$, $\angle7$ and $\angle8$; lines $d$ and $e$, transversals $a$ and $b$.
2. Alternate - interior angles: $\angle2$ and $\angle3$, $\angle1$ and $\angle4$; lines $d$ and $e$, transversals $a$ and $b$.
3. Same - side interior angles: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$; lines $d$ and $e$, transversals $a$ and $b$.
4. Alternate - exterior angles: $\angle5$ and $\angle7$, $\angle6$ and $\angle8$; lines $d$ and $e$, transversals $a$ and $b$.